Goal 4 – Multiplying and Dividing with 4s
Concrete Routines
1)
Abacus Double-Doubles – have students represent a “4-times”
problem in 4 rows. Then have students
calculate 2 rows, and then have them double that. For instance, 4x6 would be modeled on the
abacus as 4 rows of 6. Then students
would calculate 2x6=12, and then mentally double 12 to get 24.
a. Note:
Be sure to have students share their mental math strategies for doubling
double-digit numbers such as 18 doubled for 4x9=2x2x9.
b. This same activity can be done using
counters and a 10x10 grid.
Representational Routines
2)
Four-Patterns on the Hundred Chart:
Multiplication – have each
student place a marker on his/her individual hundred chart as 4s multiplication
problems are called out. Once students
have placed their markers, the answer should be provided and students’ strategies
for knowing without counting can be shared.
a.
Ask
students to predict and share strategies for determining whether a product will
be even or odd – over time, the goal is for students to realize that an even
number times any other whole number gives an even product.
b.
Encourage
students to notice the alternating pattern of 4s products ending in 4 and 8,
and then in 2, 6, and 0.
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4
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8
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12
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16
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20
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24
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28
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32
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36
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40
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c.
Encourage
students to use 4x5 as a benchmark. Ask
students to discuss how this can help them know 4x4 and 4x6 without counting.
d.
Also
encourage students to use 4x10 as a benchmark to assist with 4x9.
3) Four-Patterns
on the Hundred Chart: Division
– have each student place a marker on his/her individual hundred chart as 4s division
problems are called out. Once students
have placed their markers, the answer should be provided and students’ strategies
for knowing without counting can be shared.
Abstract Routines
4)
Clap Facts – Say a fact such as “4 fives” or “28
divided by 4” and then use a hand signal for wait. Give students 2 or 3 seconds to process, and
then clap your hands, at which time students will choral respond with the
answer.
